SOLUTION: Q25- A motorboat can maintain a constant speed of 16 miles per hour relative to the water.The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15

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Question 156526This question is from textbook Sullivan, college algebra
: Q25- A motorboat can maintain a constant speed of 16 miles per hour relative to the water.The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes.What is the speed of the current?
Q33- Working together on a job. Trent can deliver his newspapers in 30 minutes.It takes Lois 20 minutes to do the same rout.How long would it take them to deliver the newspapers if they work together This question is from textbook Sullivan, college algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Q25- A motorboat can maintain a constant speed of 16 miles per hour relative to the water.The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes.What is the speed of the current?
;
Let x = speed of the current
then
(16-x) = speed upstream
and
(16+x) = speed downstream
:
Convert 20 min to hrs 20%2F60 = 1%2F3 hrs
Convert 15 min to hrs 15%2F60 = 1%2F4 hrs
:
Distance of the two trips is the same; write a dist equation: dist = time * speed
;
1%2F4(16+x) = 1%2F3(16-x)
Multiply both sides 12 to get rid of the denominators:
3(16 + x) = 4(16-x)
:
48 + 3x = 64 - 4x
:
3x + 4x = 64 - 48
:
7x = 16
x = 16%2F7
x ~ 2.3 mph is the current
:
Check solution with a calc, confirm that the distances are equal
.33*13.7 = 4.5
.25*18.3 = 4.5
:
:
Q33- Working together on a job. Trent can deliver his newspapers in 30 minutes.
It takes Lois 20 minutes to do the same route. How long would it take
them to deliver the newspapers if they work together?
:
Let t = time required working together in minutes)
Let the completed job = 1
:
t%2F30 + t%2F20 = 1
Multiply equation by 60
2t + 3t = 60
:
t = 60%2F5
t = 12 min working together
;
:
Check solution
(12/30) + (12/20) =
.4 + .6 = 1